Republican lawmakers in several states are blunting plans by GOP governors to reduce or eliminate income taxes, putting the legislators at odds with figures many in the party see as leading voices on reshaping government.

Friction over tax policy within the GOP has flared in states such as Louisiana, Nebraska, Kansas and Ohio, as Republican lawmakers raise concerns over projected revenue losses from income-tax cuts. Three of those states shelved big income-tax cuts that would be paid for by broadening the sales tax, and in...